NASA TECHNICAL fflP^Mlt NASA TM X-1772MEMORANDUM

CMl-s.IX.

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NIGHT-! . ,CONDITIONS AND LAUNCH WINDOWS *FOR RESEARCH EXPERIMENTS

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b y Jean Q Keating . . . . . . . . . . . . . .

Langley Research CenterLangley Station, Hampton, Va.

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NATIONAL AERONAUTICS AND SPAt£ ADMINISTRATION '*• eWASH1N6fON; 0. C. • WRa 1969

https://ntrs.nasa.gov/search.jsp?R=19690013604 2018-08-06T20:51:02+00:00Z

NASATM X-1772

NIGHT-SKY-BACKGROUND CONDITIONS AND LAUNCH WINDOWS

FOR RESEARCH EXPERIMENTS

By Jean C. Keating

Langley Research CenterLangley Station, Hampton, Va.

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

For sale by the Clearinghouse for Federal Scienti f ic and Technical InformationSpringfield, Virginia 22151 - CFSTI price $3.00

NIGHT-SKY-BACKGROUND CONDITIONS AND LAUNCH WINDOWS

FOR RESEARCH EXPERIMENTS

By Jean C. KeatingLangley Research Center

SUMMARY

Darkness of the night sky background is required by many research experimentsduring various portions of their flight. A method was originally developed for theTrailblazer series to define launch windows that coincide with periods during which thebrightness of the night sky background results solely from the illumination produced bythe myriad of stars. Since this same method has proved useful to many other experi-ments as well, a general description of the method and the computer program developedto determine such launch windows are discussed. For any location between latitudes60° N and 60° S, such times of launch may be determined to an accuracy of 2 minutes.

INTRODUCTION r-,^J

For an increasing number of research experiments, maximum darkness of thenight sky background is required either during the launch of the vehicle, during the data-

gathering phase, or throughout the entire interval from launch to completion of the flight.

A method was originally developed for the Trailblazer series (ref. 1) to determinevehicle launch windows that would coincide with periods when the sky background wouldbe no brighter than the average illumination produced by starlight. During such periods,the brightness of the sky background would be approximately 2.15 x 10"^ lux (ref. 2).

This method was capable of defining such periods of darkness of the sky background toan accuracy of 2 minutes for any location between latitudes 60° N and 60° S. It wassubsequently used to determine the launch windows of many other experiments wheredarkness of the sky background was essential. A description of the method is presented

herein.

SYMBOLS

Dn calendar day

GMT Greenwich mean time

h altitude, meters

N integer

LMT local mean time

AT elapsed flight time between launch and some event with regard to flight,minute s

At difference in times of moonrise (or moonset) on any two successive days,

minute s

Az increase in zenith angle with altitude of astronomical phenomenon, degrees

X longitude, degrees

(p latitude, degrees

Xp meridian of a standard time zone at which local standard time equals local

mean time (for example, the 75° meridian of the eastern standard time

zone), degrees

6 declination, degrees

Subscripts:

E some geographic location

G Greenwich

M moon

T astronomical twilight

SKY-BACKGROUND CONDITIONS

Maximum darkness of the sky background at any specific location is assumed to

exist if the moon is below the horizon - after moonset and before moonrise - and the

sun's zenith angle is greater than or equal to 108° — after the end and before the

beginning of astronomical twilight. During such time periods, the brightness of the skybackground results from the illumination produced by the myriad of stars.

The local mean times of moonrise, moonset, and the end and beginning of astro-nomical twilight for latitudes between 60° N and 60° S at the Greenwich meridian,0° longitude, may be obtained from the American Ephemeris and Nautical Almanac(ref. 3), which is published yearly approximately 16 months in advance. From datalisted in reference 3, the times at which these four phenomena, will occur at any locationother than Greenwich are determined to an accuracy of 2 minutes for all locationsbetween latitudes 60° N and 60° S. A plot of date and times of each of these four phe-nomena results in the four curves shown in figure 1. For all times defined by pointswhich lie within the area enclosed by these four curves, maximum darkness conditionswill exist at the given location.

Twilight

The end and beginning of astronomical twilight is defined as the instant when thetrue geocentric zenith distance of the center point of the sun's disk is 108°. For variouslatitudes between 0° N and 60° N the local mean times of the end and beginning of astro-nomical twilight at the meridan of Greenwich are given in reference 3 at 5 -day intervalsthroughout the year, as shown in figure 2. Theoretically, interpolation is necessary toobtain the local mean time of the end and beginning of astronomical twilight for otherdays. Corrections for intermediate days are unnecessary, however, for the 2-minuteaccuracy requirement. On any given day Dn and for a given latitude 0, the localmean time of astronomical twilight at any meridian Xg is assumed to be equal to thelocal mean time of astronomical twilight at Greenwich:

= LMTT(xG,(/>,Dn) (1)

The local mean time of astronomical twilight at any latitude {/>g is obtained byassuming a linear interpolation between the two values of $ listed in reference 3 whichare nearer to 0g. The local mean time of astronomical twilight at a specific locationof latitude 0g and longitude Xg thus determined is denoted as LMTrpU>g,X]A

Times for astronomical twilight are listed only for northern latitudes in refer-ence 3. For southern latitudes, these times are determined by means of correctiontables given at the bottom of the page of northern latitudes, as shown in figure 2.

Moonrise and Moonset

Moonrise and moonset are defined as the instant when the true geocentric zenithdistance of the central point of the moon's disk is

90°34' + S - (2)

away from the observer's zenith where

semidiameter of moon

horizontal parallax of moon

34' atmospheric refraction

Correction for intermediate longitude.- For latitudes between 60° N and 60° S, thelocal mean times of moonrise and moonset at the meridian of Greenwich are tabulated inreference 3. The times are listed for both northern and southern latitudes. Moonriseand moonset occur later on each succeeding night by an amount which varies from about5- to 1— hours, as shown in figure 3. Therefore, a longitude correction is essential in^ 2determining the times of moonrise and moonset for meridians other than Greenwich. Tothe accuracies required by vehicle launch times, it is sufficient to assume a linear inter-polation with longitude between the time of these events on two successive days. For anygiven day Dn, the local mean time of moonrise at the meridian of Greenwich is denotedas LMT]y[(XG>$>Dn)- The corresponding time on the succeeding day Dn+j is denotedby LMTM(xG,$,Dn+i), and the corresponding time on the preceding day Dn_j isdenoted by LMT]y|(xG,0,Dn_]). Any meridian XE other than the meridian ofGreenwich is denoted by a positive sign if the meridian is west of Greenwich and by anegative sign if the meridian is east of Greenwich. For any meridian XE other thanthe meridian of Greenwich, the local mean time of moonrise for the day Dn, denoted by

],0,DnY is determined from the following equation:

where if XE > 0°

and if XE < 0°

LMTM(xE,0,Dn) = LMTM(xG,0,Dn)

At = LMTM(xG,0,Dn+1) - LMTM(xG,4>,Dn)

At = LMTM(xG,0,Dn) - LMTM(xG,0,Dn.!)

(3)

Correction to intermediate latitudes.- For each of the two values of <p listed inreference 3 that are nearer to 0E, the local mean times of moonrise or moonset atXg are determined from equation (3). A linear interpolation with latitude is used to

determine LMTM(^Ej0E>Dn> the local mean time of moonrise or moonset at the givenlongitude and latitude. If the local mean times of moonrise, moonset, and the end andbeginning of astronomical twilight thus calculated are plotted against date (as shown infig. 1), the area enclosed by the four curves then defines the local mean times whendarkness conditions will exist for that given location.

Altitude Corrections

The foregoing procedure determines the local mean times at which moonrise,moonset, and the end and beginning of astronomical twilight will occur at ground level.An increase in altitude produces an increase in the geocentric zenith angle necessary toattain similar conditions of illumination. This increase in zenith angle (in degrees) withaltitude (in meters) is

Az = 0.0321 /h (4)

for small values of Az. (See, for example, ref. 2.) The elapsed time required to attainthe increase in zenith angle Az given by equation (4) is dependent on both the latitude ofthe location and the apparent declination of the celestial body. For extreme altitudes andlatitudes such corrections are very complex. If altitude is a factor, use of the methoddescribed herein should be limited to cases where the latitude of the location is between45° N and 45° S and values of Az from equation (4) are 3° or less.

Altitude corrections for moonrise or moonset.- For small values of Az, a changeof Az degrees causes a difference in times of rising and setting of the moon ofAAz minutes (ref. 2) where

A A 1*f 2^ - 2* V1/2A = 4.14(cos*0 - smr6M)V • JM)

The value of the factor A is dependent on the apparent declination of the moonwhich varies with time. For latitudes between 45° N and 45° S, the value of A neverexceeds 8.0, however. In the program described herein, a constant value of A equalto 8.0 is used to eliminate the need for defining the value of 6jvj. This altitude correc-tion of 8 Az is added to the time of moonset and subtracted from the time of moonrise.

This approach gives a conservative accounting for the moonrise and moonsetconditions for altitudes less than 9000 meters and latitudes between 45° N and 45° S.Geometry problems encountered for other latitudes and altitudes exceed the scope of thissimplified approach. Thus, this method should not be used for altitudes greater than9000 meters or for values of </>E greater than 45° N or less than 45° S.

Altitude correction for astronomical twilight.- The illumination produced by thesun should be the problem of greatest concern. Based on data from reference 2, theillumination of the sky background which exists at various zenith angles of the sun isshown in figure 4. The times of three twilight conditions at the Greenwich meridian arereadily available in the form of tabulations from references 3 and 4. They are as fol-lows: (1) civil twilight, corresponding to a sun's zenith angle of 96°; (2) nautical twi-light, corresponding to a sun's zenith angle of 102°; and (3) astronomical twilight, corre-sponding to a sun's zenith angle of 108°. The third condition, astronomical twilight, wasused as a boundary condition for the launch windows. As shown in figure 4, the illumina-tion of the night sky background produced by the sun at astronomical twilight is approxi-mately 6.7 x 10~4 lux, a value which is less than the illumination produced by starlight.Thus, at a zenith angle of 105°, the illumination produced by the sun is still less than thatresulting from starlight and the altitude correction for twilight may be omitted where Azis less than 3°. This corresponds to an altitude of 9000 meters or less.

LAUNCH WINDOWS

In general, the need for darkness conditions by any particular experiment shouldfall into one of three basic categories. Darkness of the night sky background might berequired (1) during the launch operations of the flight, (2) during some data-gatheringphase or reentry phase occurring downrange, or (3) during the entire interval fromlaunch to termination of the flight. The geographic location of the particular event isused to determine the local mean time at which maximum darkness conditions will pre-vail for that location. To be of any practical use, however, these local mean timesmust be expressed in terms of some standard or clock time, either Greenwich or thelocal standard time of the launch site. The local standard time must be corrected by afactor of AT to account for the elapsed flight time between launch and the arrival of thevehicle at a particular point downrange.

Vehicle launch times are defined as the intervals during which the launching of thevehicle will insure that the occurrence of some particular portion of the flight will coin-cide with maximum darkness of the sky background. Such times are expressed as plotssimilar to figure 1. The area enclosed by the four curves is called the launch window.

Conversion to Local Standard Time

The Greenwich mean time GMT at which moonrise, moonset, and the end andbeginning of astronomical twilight will occur at a specific location ($E,XE) *s determinedby adding the equivalent of Xg expressed in time to the local mean time of these events.Thus,

GMT = LMT + r-j (5)15

The times of maximum darkness conditions at some point (<£E>XE) in terms of any stand-ard time are as follows:

LST = GMT - U^) (6)\15/

where Xp is the prime meridian for the standard time zone.

Determination of Launch Windows for Three Example Conditions

As outlined previously, the needs of various experiments will dictate the locationsfor which darkness conditions are necessary. However, most of the factors likely to beinvolved in the determination of launch windows for any individual experiment can beillustrated by the following examples. The information necessary for the determinationof these example launch windows was given previously in figures 2 and 3. The groundtrack of a vehicle which will be used as an example is shown in figure 5. It was con-sidered to be launched from NASA Wallops Station along a flight azimuth of 130°. AtAT = 660 seconds after launch, reentry occurred at Q, a point downrange at latitude30° N and longitude 65.3° W. Darkness of the night sky background might be required(1) during the launch phase only, (2) 660 seconds after launch when the reentry occurredat Q, or (3) during both launch and reentry. The launch windows which satisfy each ofthese three conditions are shown in figures 6.

Maximum darkness conditions during launch.- Of the three example conditions,the simplest to determine is the launch window for maximum darkness during the launchphase of the flight. The local mean times of moonrise, moonset, and the end and begin-ning of astronomical twilight are determined for the coordinates of the launch site andconverted to the desired standard times. The correct launch window is obtained byplotting the standard times of these four phenomena against date. The launch window forthis condition, in eastern standard time, is represented by the area enclosed by thedashed curves in figure 6.

Maximum darkness conditions downrange.- Other experiments may require dark-ness conditions at some geographic location and time other than launch - for example,during the reentry or data-gathering portions of the flight. The determination of launchtimes which insure that this downrange event occurs during periods of maximum dark-ness is similar to that for the maximum darkness conditions during launch. Times ofmaximum darkness conditions are determined for the latitude and longitude of this down-range event rather than the launch site, and they are corrected to the desired standardtime. But for this case, an additional correction must be made for AT, the elapsed

time in flight between launch and the downrange event. The local standard times ofmoonrise, moonset, and the end and beginning of astronomical twilight must be correctedby -AT. The launch window is obtained by plotting these corrected times against date.The eastern standard times of these four limiting conditions at Q are corrected by-AT of 11 minutes to obtain the correct launch window, which is represented by the areaenclosed by the solid curves in figure 6.

Maximum darkness conditions during entire flight.- For still other experiments,maximum darkness conditions are necessary during the entire interval from launch totermination. The launch window which satisfies these conditions is obtained by treatingthe problem as a combination of the two previous cases. The launch window insuringmaximum darkness conditions at launch is computed as previously described and repre-sented in figure 6 by the dashed curves. A second launch window, insuring maximumdarkness conditions at the end point of the flight is then computed and superimposed uponthe previous plot. Maximum darkness conditions will prevail during the entire intervalof the vehicle flight so long as the vehicle is launched during any time within the enclosedarea of both windows, which is represented by the shaded area of figure 6. Maximumdarkness conditions would exist at ground level during the entire interval of the groundtrack shown in figure 5 so long as the vehicle was launched from NASA Wallops Stationduring the launch window represented by this shaded area of figure 6.

APPLICATION OF METHOD

Frequently, difficulties with wind and weather conditions, with the vehicle, or withthe payload may cause delays in the countdown. It is often desirable to know what sacri-fices, if any, would be made by exceeding the limits of a given launch window by a fewminutes. In the procedure discussed herein, the points which lie within some of theindividual windows but are not common to all are effective in determining critical fea-tures associated with exceeding the limits of the launch window.

In the launch windows discussed in the preceding section, the points which liewithin the areas of one or the other of the windows, which insure maximum darknessconditions at launch or reentry but are not common to both, may be roughly divided intofour areas. These four groups are designated by the letters A, B, C, and D in figure 6.

The significances of the launch times represented by points which lie within thesefour groups are as follows:

A maximum darkness conditions would exist at reentry but launch would takeplace prior to the end of astronomical twilight at the launch site.

B maximum darkness conditions would exist during launch but reentry wouldoccur after the beginning of astronomical twilight

C maximum darkness conditions would exist during launch but reentry wouldoccur after moonrise

D maximum darkness conditions would exist at reentry but launch would takeplace prior to moonset

In the example case, the vehicle was assumed to be launched from NASA WallopsStation toward the southeast. Thus, launching the vehicle at some time earlier than thenominal launch window, as represented by points in groups A or D, would be more desir-able than an extension of the launch time into area B. No extension of launch time intoarea C could be tolerated.

For any particular experiment, darkness conditions might be required at one, two,or more locations. Regardless of the number of locations at which darkness conditionsare needed, the launch window may be obtained by extending the method described pre-viously. Darkness requirements at N different geographic locations and times duringa flight would result in N individual windows. The launch time which would insuremaximum darkness conditions at all N locations would be represented by points incommon to all N windows.

COMPUTER PROGRAM TO DETERMINE LAUNCH WINDOWS

The use of a computer is a big time-saver where launch windows-at several dif-ferent sites are needed, since the basic information from reference 2 necessary for thecomputations can be programed once and reused. A program for this purpose waswritten in FORTRAN IV for use with the Control Data 6600 computer system at LangleyResearch Center. Inputs required by the program are listed in the appendix and includethe times of the various astronomical events at the Greenwich meridian, the longitude ofthe location at which darkness conditions are required, the prime meridian of the stand-ard time in which launch windows will be expressed, the elapsed flight time from launchto occurrence of the event, and the altitude for which corrections to moonrise and moon-set are to be made. No corrections are made for intermediate latitudes.

A listing of the program and the inputs for and printout of data necessary to deter-mine the launch window defined by the solid line in figure 6 are given in the appendix.Input values for latitude and altitude are tested by the program. Those in excess ofvalues for which this program has been defined to be applicable will cause the programto abort.

CONCLUDING REMARKS

The method described herein has proved useful to many research experiments indetermining launch windows which coincide with periods of maximum darkness of thenight sky background. During such time intervals, the brightness of the night sky back-ground results from the illumination produced by starlight. For any location betweenlatitudes 60° N and 60° S, these time intervals may be determined to an accuracy of2 minutes by this method.

Langley Research Center,National Aeronautics and Space Administration,

Langley Station, Hampton, Va., Dec. 31, 1968,715-02-00-01-23.

10

APPENDIX

COMPUTER PROGRAM TO DETERMINE VEHICLE LAUNCH WINDOWS

In order to speed the calculations of launch windows, the method described in thetext was incorporated into a computer program (A2259), written in FORTRAN IV for usewith the Control Data 6600 computer system at the Langley Research Center. A com-plete listing of the program is given in table I. The inputs required by the program areas follows:

HOUR (I, J)

LAT, ALONG, CORR, KEY, DRTC, ALT, ISIGN

/ DAY (I)

N, ICODE

1. N, ICODEFormat (14, 12)

N specifies the time interval in days for the particular case.

ICODE is used to distinguish whether computations deal with sun or moon.ICODE = 2 signifies twilight conditions; ICODE = 0 signifies moonrise ormoonset conditions.

2. DAY (I)Format (1814)

DAY array provides a 4-digit designation of the date; that is, March 7 is shownas 0307.

11

APPENDIX - Continued

3. AFormat (12A6)

A array provides a 72 field label available for case identification on printout.

4. LAT, ALONG, CORK, KEY, DRTC, ALT, ISIGNFormat (13, 2F6.1, 13, F6.1, F10.1, 12)

LAT gives the latitude for which moon and twilight conditions are required.

ALONG gives the longitude for which the times of moon and twilight conditionsare required. West longitude is denoted by a plus; east longitude, by a minus.

CORK is the prime meridian Xp of the standard time in which launch windowswill be expressed. For example, CORR value used to obtain launch windowsin eastern standard time would be 75°.

KEY is used to indicate computations that should be repeated for different lati-tudes using the same dates in the DAY array. KEY 0 causes program torepeat for a second latitude.

DRTC gives the correction for elapsed flight time from launch to the occurrenceof the downrange event, AT. The value of DRTC used as input to the programmust always be positive.

ALT denotes the altitude in meters for which moonrise and moonset are to becorrected.

ISIGN is used to designate whether computations deal with moonrise or moonset.ISIGN = -1 indicates moonrise; ISIGN = 1 indicates moonset.

5. HOUR (I,J)Format (3612)

HOUR array denotes the local mean time of twilight or moon condition atGreenwich. Information is punched in form given in American Ephemeris andNautical Almanac (ref. 3), in hours and minutes.

12

APPENDIX - Concluded

The launch window defined by the solid curves in figure 6 may be determined frominformation found in figures 2 and 3. This same information in the form of inputs to thecomputer program is shown in table n. The output which would be obtained from theseinputs is shown in table HI. A plot of this output results in the launch window defined bythe solid curves in figure 6.

Use of input values for altitude in excess of 9000 meters will cause the program toabort and result in a printout similar to the one shown in table IV. Use of input valuesfor latitudes greater than 45° N or less than 45° S when 0 < h ^ 9000, will cause the pro-gram to abort and result in a printout similar to the one shown in table V.

13

REFERENCES

1. Gardner, William N.; Brown, Clarence A., Jr.; Henning, Allen B.; Hook, W. Ray;Lundstrom, Reginald R.; and Ramsey, Ira W., Jr.; Description of Vehicle Systemand Flight Tests of Nine Trailblazer I Reentry Physics Research Vehicles. NASATN D-2189, 1964.

2. Anon.: Explanatory Supplement to the Astronomical Ephemeris and the AmericanEphemeris and Nautical Almanac. H.M. Nautical Almanac Office, 1961,pp. 398-406.

3. Anon.: The American Ephemeris and Nautical Almanac for the Year 1968. U.S. Nav.Observ., 1966.

4. Anon.: The Air Almanac. U.S. Nav. Observ., May-Aug. 1967.

14

TABLE I.- LISTING OF COMPUTER PROGRAM

HXUGR AM "A2259< INPUT , UU I P'J f , T A P E 5= 1 Nf 'UT , T APE6=C)oT PUT )INTEGER "DAY f7)ATE7HOUft~,T TM'E ,"OETT~AT7fa~wl

D I ME N S I 0 N~D~AY"( 3 65 ) '," DA T E ("565 ')7HOJJRT3 6372TtTTHF( "3 6 5 >TO £ L T AT~( 3~6 5TC ICODE~SPE(nFrE^"WWETHER"V1OnN~CrR"-SUN~BElNC — • nrODE~^-Z - SUN

.. ICOOE ="C " '-C KEY~"N'qT~£"QtfATrTO~ZE'fta I NDICATES~C~ASTT~TG~ BE~ "RgPE AT £0' uS IMG S A M C "C _ _i jMTES_JOK RLFF EK'ENT~L'A'TTTUiyE ' ""c _ ...... " ..... "'__ _ ' _." ........ ~ ___ ~" ~_ _ ...... " ..... "c " ............ ~~~ ", AL"T"= "ALTifuoE IN MET"E"R"S .....

" C DRTC =" 0 OH N RANGE 11 HE' COR R EC T H JN 1 N' H I NU T'ES""C " ""ISJGN_= -1 FOR MOONRITE AND »1 FUR M"7" <* K E A 0(5 ,'l'd 0 1 N t IC OP £" 100 FQRMAT(T4,12)

- ••~5"'ftEA'p'C57TO'nTD7nrm v i = i, NI101 F 0 rt M'AT"C1"8'I ~)~

"" " R E AD ("5 tT03") A103 FORMAT(T2A6") '.3 00 R11A0 ( 5 , 102")"( rAT77TLO"i>ifGTC"0^ ","K"ErrDRTC t ALT .102 FORMAT (r

.•< E A D ( '5't'i'OVl' ( ("H OUR ( I', J ) ,"j= 1 , 2") t 1 = 1 1 N )1 0"4 " F 0 R M A T <3 '6\~ZY~ ~_

W K I'T E"( "6","20lD"A2 0"0 F 0 3 M A T ( 1 H lTr2"A"6"/71

~ Hf<ITE(6V20T)DRTCTAL~r,TSTGN2 03 " 'FOR "M AT ( 1HOT2TH"DDWN R A.NG

1 X 2 4 H S G O D F V n n [ T D C K'R~.~=TI'21~WRITt"(6,201 ILAT, ALONG, CllRR

2 Of FURf^T(lW31<TrirATITWE7X9^^17XF9VlV/7/'2yilH"STAN^ARDnrrMF7X'4T(D"ATF/r2X'fflHQU^^2HDAY/ / )" """ __ _" __ ~ __ "~""" ...... " * ..... ~~~__ ~"

D'()""1'0""M="17N~ TO M INUTErK)=(HDW("M7r)*60')>"HD"UH'rM721

E 0 . 2 ) GOT 0 6~ f. ALT="8T*70T2T*TQ~RT(~ALT) *~FL'O'ATTTSTGNT'"" I f (TAT. GTT6l5")~~G a~TO~VO" IF -TALTTLTT70Tri;-0~~Ta~7 r~~

) GO'" ' IF( L A r . G T . " 4 i > ) GO T07 " J=.l '" ..... ' - ....... — '

DO 1VO K=l,IN ' " ...... . . . - . . . - — ...... - ...... ...... -- .. . . .

I F( M I NUTG( K '«• 1 y."GT".M"INUTE ( K ) ) GO "~TQ~~3~Q~ ....... " ........ "M INUTEIK + 1 } =MINUTC(K4:lH-l''<'tO " ...... ------ ....... " ........ "HEL T AT ( K ) = F LOAT ( MINUTE ( K> 1) -M I NUT'F(XT)"*"ArONG/3"6"0". ......

- R A W T ( K ) =MI N_UTE (K . r^-OELTAT ( K ) >I FIX TTArD'NG-CQRRl V.-DRTC^CALT)"M i 'N u 1 1 ( "K+ n =MTNIF (RA'WT'{XT7'GT".~OT~G'0'~TO~TT 1 1': r ( K ) =RA W T ( K ) «•"OAf i: (K) =DAY { J-l )GU ID 3 ""

15

TABLE I. - LISTING OF COMPUTER PROGRAM - Concluded

IF ( RAW T ( K ) . LT . 1440> 'GO TTT"Z"T I'M t ( K ) VfUvTr rK)-1440

J»~lTGO TO 3T I M E ( KT=R AWT( K")OAT E ( K)=DAYT3)J = J + 2

" GO" TO~Y5~30 OEL TA'T( K ) = F L~0 ATTM INUTTTK+ ll -.iTNUT E ( K ) ) *AL ONG/T6D ...... ~K'AH T ( K ) =MINUTb ( KT+D'ELTA"T ( X )"+! FTXT<" I f( A A w T ( K )VG T .'0')~GO TQ~5 0

r I'M t ( K ) = RAa'T ( XT* r44"0' 0 A T F ( K ) = DAY'CJ-'lT"" "\VO" TO 7"6"50 ~ I F ( K AWT ('K")71TT~.T4~40) GO TO~6D

T 'I M E ( K ) = R A w TOAT E ( tO =GO 10 70

60 T I ' M f e ( K'_

70 J-J-H '"75"'M=0 [J^ _JB"0'"[F"<'TIME('K')T'LTT6'0) GU TO

M=M'+1 . . . . . . .TIME (Ki=TlME(K)-6D~

~"90 WKI T E ( 6 ,202Tff2 0 2 " F 0 R M A T ( I 5V4>! t f41 8'X, 15)

I F'( KEV".'£'Q'.~0~)'~C'D~TO 'tGO .TO 300"

6 IF( LAT.Gf. '6 'O") GO TO 40 "'I F t A L T . G T . 9 0 0 0 . ) GU TO ^5D! 1 20' VK=Tf"Nf ~ ~ " _' ""f)AT F ( K) =OAY {K) " " ~"RAW T ( K ) =MI NUTE'( KI +|)EUTAT (XT'*-' IF IXTrA'tD'N'G-COft'R) <"t .-OK TC)

""M=0 ~ : """i 3 " IF ( F A W T"{"K) .LT."60)~GUTQ'2 0

RA-.-»T (X) =r~ " "GO TO 25; 20 "WRI l><6,2021"'MV^TjKT;OATFrK)"

I" GU TO 8 ~"~^___ ~_2. ..

- !'1 AI (_l 19 5 X 2 7ffi-A »'fUUE'""E'XC E E DS"~60~i)E'G~R EESTGO TO "8

145 "WK I T E ( A ,"20"5 )1205 FORMAT!1H05X28HALTITUUE EXTEEOS 9000 METERS)

"GO TO 8

; 4 6 " W R ITE (6 ,206 ) _ . . _ _ ' ~ ~\2Qh"TORMArrrroTX37HLATITUOE TXCFEDS 45 FOR ALTITUDEi " H . f F ("KE Y. EQ. 0) GO TO 4" _GO TO "TOO55 CONTINUE"

END"

16

TABLE H.- COMPUTER-PROGRAM INPUTS FOR SAMPLE CASE

160114011501160117011801190120012101220123012401250126012701280129

MOONRISE BEGINNING JAN. 14,196830 65.3 75.0 11.0161017111814191920222125222823320037014502550404051006080658

18012701280129013001310201020202030204020502060207020802090210021102120213

MOONSET BEGINNING JAN. 27,196830 65.3 75.0 11.015101617172418301932203021262221231500100106020303010358045105400623

6 2010501100115012001250130BEGINNING OF ASTRONOMICAL TWILIGHT - BEGINNING JAN. 5, 196830 65.3 75.0 11.0053105320533053205320531

6 2010501100115012001250130

END OF ASTRONOMICAL TWILIGHT - BEGINNING JAN. 5, 196830 65.3 75.0 11.0183918431846184918531857

17

TABLE HI.- OUTPUT OF COMPUTER PROGRAM FOR SAMPLE CASE

MUUNRISE BEG

OOWNRANGE T I M EALT

LATITUDE

30

STANDARD T I M EHOUR MINUTE

15 3216 3317 3618 '.I19 -»4

, 2 0 4 721 50 '22 54

"24 0I 32 18

" 3 26 ~4 31

" 5 T ""~28-

"IN.NING JAN. 14,1968

CORR. =' 11.00ITUDE = 0.0 SIGN OF ALTITUDE COkR. =-0

LONGITUDE STANDARD TIME

65.3 75.0

DATEMON. DAY

•..-

114115 .116117118119120121122124125126127128

18

TABLE HI.- OUTPUT OF COMPUTER PROGRAM FOR SAMPLE CASE - Continued

MOONSET BEGINNING""JAN. "27, 1968

OGWiNRANGI: T 1M£ CORK. = 11.00""ALTITUDE"= OVO SIGN" OF "ALTITUDE"CORR

LATITUDE L ONGITUO E~^ ST AWAR D~ T TMF"

TO 6573 75". 0

_STANDARO T IME DATE"HOUR MINUTE RUKT. DA~¥~

12T

Zi i58 212

19

TABLE HI.- OUTPUT OF COMPUTER PROGRAM FOR SAMPLE CASE - Continued

t i lGlNNING OF " A S T R O N O M I C A L " Tu lL ' IGHT" -"BEGINNING"" JA'N.' "S,

GC TIMi ; . COHrt. ' = 11.00A L T I T U D E ^ 0.0 " S I G N OF "ALTITUDE COKK. =-0

LAT ITUDE •"-"" LONGITUDE " " S T A N D A R D TIME

STANDAKD TIME" ~" " DATEHOUK MINUTE MON. OAY

5455 11055 " 11 5

__53 _ 125~52~~ 130

20

30 "" " """ 65.3 75VO""

TABLE m.- OUTPUT OF COMPUTER PROGRAM FOR SAMPLE CASE - Concluded

EML) UF ASTKUNlMfCAL TWILIGHT - tiETGTNNfNG J'A'NT"?", 19~6a

TIME'CORR". =~Tl.O"0~ALTTTUDE~= IT, T I T U

L A T I T U D E

._._ ...3flj

STANDARD TIME_HOUR """ MI MUTE

"18""1818 -

"18"1618

Tl

LT)NGTTUD~E~ ST"A'NDA'R"D~TTMT

5573 75. (T

DATEMOM. DAY

"105"110'ITS'1 20"1"2'5

21

TABLE IV.- SAMPLE OF OUTPUT OBTAINED IF INPUT VALUE

FOR ALTITUDE EXCEEDS 9000 METERS

MUGNKISE BEGINNING JAN. 14,r96"8"

:00*NRANGE T I ME" "CORK"." = 11.00ACTITOD"E~=~~TO"OT)'OVO~

L A T I TUOE ITONGTITODI STAWA~RD~TT>TE~

STANDARD TIME DATEHOUR MINUTE MON. DAY

ALTITUDE ~ E XC E E D3~VO()"0~ METFRST

22

TABLE V.- SAMPLE OF OUTPUT OBTAINED IF INPUT VALUE

FOR LATITUDE EXCEEDS 45° FOR CASE WHERE

ALTITUDE CORRECTION IS TO BE APPLIED

MCKJNRlSE 1 BEGINNING JAN.

DOWNRANGfc T IME CORR. = 11.00""" '"" "ALT ITUOE""= TOOOTO""STGN~aF~A^TTTUf)"E~COf<R".~"=-T

L "ATI T UP E ' LONG t TOOT

50 65.3,

STANDARD TIME DATEHOUR M T N U T E M O N . D A Y

23

s'rH

i?

S 13S

M 15TW 17T

F 19

S

S 21-

M

T 23

W

T

F

S 27

S

M 29]T

W 31-

T

F 2

S

S 4

M

T

W

T

F

S . 10-

S

M 12

End ofastronomical•

. _ twilight ; ; /

Moonset

Moonrise

Beginning ofastronomical

twilight

1800 2000 2200 2400 0200

Local mean time, hours

04.00 0600

H

16

18

-20

-22

24

26

•28

30

1

3

5

7

9

11

J13

In

I

Figure 1.- Time interval during January-February 1968, when the illumination of the sky background atlatitude 30° N and longitude 65° W will result only from starlight.

24

SUNSET AND TWILIGHT, 1968

LOCAL MEAN TIME OF SUNSET AND END OF ASTRONOMICALTWILIGHT—MERIDIAN OF GREENWICH

\^Lat.Date^^^

0° +10° 420° +30° +35° +40° +45° +50° +52° +54° +56° +58° +60°

SUNSET (UPPER LIMB)

Jan. 05in1520

2!)30

Feb. 4!)14

192429

Mar. 510

15202530

Apr. 4

h mIS 07IS 09IS 1 1IS IHIS Mi

IS 1C.IS 1718 1718 ISIS 18

1S 17IS 1718 l(i18 1518 14

18 1218 11180918 081806

h m17 4917 5217 5517 57IS 00

18 02IS 0118 0018 0718 OS

18 09IS 1018 1118 1118 11

18 1118 1118 1118 1118 11

h m17 311 7 3417 3717 4117 44

17 4717 5017 5:i17 5fl17 B8

18 01is o:iIS 05180718 08

18 1018 1118 1218 1418 15

h m17 1017 1417 IS17 2217 20

17 3017 3517 3917 4317 47

17 5117 5517 5818 0218 05

180818 1118 1518 1818 21

h m}6 5S17 021 7 0(i17 II17 Hi

17 2117 2C>17 3117 3017 41

17 4017 501 7 5517 5918 04

180818 1218 1018 2018 24

h in10 441C) 481 (I 5,'i1 C> 5817 04

17 1017 Hi17 2217 2S17 3-1

17 3917 4517 51175018 02

180718 1218 1718 2218 27

h tn10271 0 3210 37IC> 4310 50

Hi 5717 0417 1117 IS17 25

17 3217 3!)17 4C>17 5317 59

18 0018 1218 1918 2518 32

h m100710 1210 IS1 0 2510 33

10 41Hi 41110 5817 0017 15

17 2417 3217 4117 4917 57

180518 13182118 2918 37

h m15 571 0 0310 091(1 1710.. 25

1 0 341C) 4210 5217 0117 10

17 2017 2917 3817 471756

180518 1318 2218 3018 39

1. m1 5 4015 5215 19100710 10

10 25Hi 3510 451 0 5517 05

17 1517 2517 3517 4517 54

18 0418 13182318 3218 42

h m15 341 5 401 1 4815 501 0 0(1

1C. 101C> 271C) 3810 4!)17 00

17 1117 2117 3217 4317 53

180418 1418 2418 3418 44

h m15 2015 20|r, •{!-,

15 4415 55

10 0010 171 C. 29104116 53

17 0517 1717 2917 4017 52

180318 1418 25183718 48

h m15 0315 1015 1')1 5 3015 41

1554100716 2010 3310 46

10 5917 1217 2517 381750

180218 1518 2718391851

KND OF ASTRONOMICAL TWILIGHT

.Inn. 05101520

2530

Feb. 4914

192429

Mar. 510

15202530

Apr. 4

li nl!l I!'.!19 2119 2519 2719 28

19 2919 2919 2919 2919 29

19 271 ) 27I ) 251 ) 241 t 23

1 ) 21J ) 2019 1819 1719 15

h n19 0119 0719 1019 1119 14

19 1519 1719 1819 1919 19

19 2019 2019 2111) 2119 21

19 2119 2119 2119 211921

h nIS f,(IS 52IS 55IS 5819 01

19 0319 0619 0819 1119 12

19 1519 1719 IS11) 2019 21

1 9 2319 2419 2019 2819 29

h liis :i.ris :nIS 4318 4018 49

18 5318 5719 0119 041908

19 119 159 IS9 219 24

9 289 319 3519 3919 42

li n1 S 2!1 S 321 8 3(118 4018 44

184918 53185719 021906

19 1119 1419 1919 231928

19321 9 3719 4119401951

h nIS 21IS 2f18 2!18 34IS 39

18 4418 4918 5519 0019 05

19 1019 151 I 211 ) 2(11 ) 32

1 ) 371 ) 431) 4919 552001

h Mis i:tIS IS18 22IS 2718 33

18 3918 4518 5218 5S19 04

19 1019 179 24i) 319 37

9 449 519 5920 0620 15

h nIS (1C18 1018 1518 2118 28

18 35IS 4118 4918 5619 04

19 1219 201 9 2919 3719 45

1!) 5420 0320 1220 2320 33

h n1 S 0'.!i s os18 1218 1918 20

18 33184018 4818 5019 04

19 1319 221 9 3019 4019 49

1 9 5920 OS20 1920 3020 42

li n1 7 5!IS (M18 1018 1618 23

18 3018 3918 4718 5019 05

19 1419 2319 33li) 4319 53

20 M20 1520 2720 392052

li in17 5(1IS 0018 0718 1318 21

18 2918 3818 47185619 00

19 1019 2519 3019 4719 58

20 1020 2320 3520 4921 04

1) Ml

1 7 5217 5(1IS 0318 1018 19

18 27183618 4618561900

19 1719 2819 4011) 5220 05

20 172031204521 0221 19

h in17 4817 5317 59180718 15

18251835184618501908

19 1919 3119 4419 5820 11

20 2520 4120 5821 1621 36

SOUTHERN LATITUDES (July to October)

For dates on first line below, enter tables above with dates on second line,and apply the correction (in minutes) given on the third line.

Date July 1 6 11 16 22 27 Aug. I AUK. 7 12 17 22 28 Sept. 2 Sept. 7 12 17 22 27 Oct. 3 Oct. 8Use Jen. 0 6 10 II 20 25 Jan. 30 Feb. 4 9 14 19 24 Fob. 29 Mar. 6 10 16 20 26 Mar. 30 Apr. 4Apply 4-1 0 -2 -3 -4 -6 . -7 -8 -» -10 -11 -12 -13 -14 -14 -14 -U -18 -U -16

(a) The GMT of sunset and end of astronomical twilight.

Figure 2.- Sample pages from the American Ephemeris and Nautical Almanac (ref. 3).

25

SUNRISE AND TWILIGHT, 1968

LOCAL MEAN TIME OF SUNRISE AND BEGINNING OF ASTRONOMICALTWILIGHT—MERIDIAN OF GREENWICH

^\. Lat.0° +10° +20° +30° +35° +40° +45° +50° +52° +54° +56° +58° +60°

SUNRISE (UPPEIl LIMB)

Jan. 05

101520

2530

Feb. 49

14

19242<>

Mar. 510

15202530

Apr. 4

h m5 59601004606607

6006 106 106 116 11

6 116 10609608607

606604603601600

h m6 166 IS6 20621622

6 236236 226 216 20

6 196 176 156 126 10

6076046015 585 56

h m035636637638638

637fi 376 356 336 30

6276 246 216 176 13

6096046005 555 51

h m6556576 576 576 56

6 546 526496 466 42

6376326276 226 16

6 10604558552546

h m708709709708706

7047016 576536 48

6 436376 316 246 18

6 116045575 50543

h m7 227227 227 20718

7 157 117077 016 60

6 496 42635627620

6 126045 565475 39

h m7 387 387 377 35

. 732

7 287 237 187 11704

6 566 486 406 316 22

6 136035 545 456 35

h in7 597 587 567 537 49

7 447 387 317 237 14

7056566466 35625

6 14603552541530

h in808808805802757

7517457377287 19

7 09659648637626

6 146035515 40528

h m8 198 188 168 12806

8007 527 447 34724

7137026516396 27

6 15603550538526

h in8328308 278 228 16

8098007 517 417 30

7 187066 516416 28

6 166026495 366 23

h in8468448408 35

• 828

8 198 107 597487 36

7 247 116 586 44630

6 16602548534520

h m9039018 568 49841

8318218097 577 44

7 307 167016 47632

6 176025475315 16

BEGINNING OF ASTRONOMICAL TWILIGHT

Jan. 05

101520

2530

Feb. 49

14

192429

Mar. 510

15202530

Apr. 4

h m4 444 464494 514 54

4 554 584 58500500

5015005004 594 58

4574 564 544 534 51

h m501503505507508

5 105 105 105 105 10

508507505503500

4 584 554 524494 46

h m5 155 185 195205 21

5215215 205 185 17

5 145 11508505501

4 564 524 484 42438

h m5 305 315 32533532

5 325315285 256 22

5 185 13508504458

4 514 454 394 324 20

h m5 365385395395 38

5375 355 315 28524

5 19. 5 14

5085024 55

4 484 404 334254 17

h m5435 455 45545544

5 425 395 355315 26

5 195 145064 594 51

4434 344 264 17408

h m5515525535515 49

546542538532527

520512504455446

4374264 16405354

h m600600559558555

5515 465 415 34527

5 195095004494 39

4 274,154033 503 36

h m6026036026015 57

5545 485 41535527

5 185084 584 464 35

4 234 103 573 433 28

h m606607605604559

5555505435355 26

5175074 554 444 31

4 174043 603 343 18

h m6 106 10609606603

5 585 51544535526

5 165054 534404 26

4 123 57341325306

h m6 146 146 12609605

5 595 535 45536526

5 145024 494 364 21

4053493313 13253

h m6 186 186 166 13608

6015 545 465 355 24

5 135004 454304 14

3 573 393 202 58236

SOUTHERN LATITUDES (July to October)

For dates on first line below, enter tables above with dates on second line,and apply the correction (in minutes) given on the third line.

Date July 1 « 11 18 22 27 Aug. 1 Aug. 7 12 17 22 28 Bcpt. »Sept. 7 12 17 22 27 Oct. 3 Oct. 8Use Jan. 0 8 10 18 20 25 Jim. 30 Fob. 4 0 14 10 24 Fob. 29 Mar. 8 10 15 20 25 Mar. 30 Apr. 4Apply +1 0 -2 -3 -4 -6 -7 -8 -9 -10 -11 -IS -13 -14 -14 -14 -15 -IS -16 -16

(b) The GMT of sunrise and beginning of astronomical twilight.

Figure 2.- Concluded. .

26

MOONRISE, NORTHERN LATITUDES, 1968

LOCAL MEAN TIME OF MOONRISE (UPPER LIMB)MERIDIAN OF GREENWICH

\ Lat.Dat*>\^

Jan. 01234

50789

1011121314

1516171819

2021222324

2526272829

3031

Feb. 123

45678

910111213

141516

0°

li m0 117 138 110029 49

103211 1311 53123313 14

135814 4515 3510 2817 23

18 1819 122003205221 39

22 2023 13

002055

1 512623 55457556

650739824907947

102811 0911 51123713 25

14 1715 1116 0617 011754

184519342022

+10°

1> ni6347 348289 10958

10 3711 1311 4912 251302

13 4214 2015 141 6 001701

17 5818551950204321 35

222623 19

0 131 10

2 103 144 175 186 15

7057 508319099 45

10 21105811 3712 191305

135514 4915 4516421739

183419282021

+20°

h m0587 608479301008

10 4211 1411 4512 171250

1320140014 5115 421637

17 30183019 35203321 31

222723 25

0 241 26

2313 374 425 42635

7 218 028389 119 43

10 1410 4711 2212 0012 43

133114 2415 22162217 23

182319 222020

+30°

h ni7 208 229089 4010 19

10 4811 1411 4112071236

130713 4314 2515 1416 10

17 1118 1419 19202221 25

222823 32

0371 45

2554045 10608658

7 408 158469 149 40

1007103511 0511 3912 18

130413 50145515 581704

180919 1420 19

+35°

h ni7 428 300 209 5510 25

10 5111 1511 3812021227

1250133014 101 4 581553

16 551801190920 1621 22

22 2923 36

0 451 56

3094 205 276247 12

7518 238509" 15939

100310 2710 5511 201203

12 4713 40143915 451653

180219 1020 18

+40°

li ni8 018 6393410 001032

105511 1511 3511 5612 18

124413 1513 521439153-1

163817 471858/200921 19

222923 40

053209

3 254395 406 437 28

8038328569 17937

95810 1910 4311 1211 46

122913 20142115 281640

17 53190520 17

+45°

li in8249 149 5110 191041

10 5911 1011 3211 4812 07

122912 5013 3114 1015 11

16 1717 291844200021 15

223023 46

1 032 24

3455026 10705746

8 178429 029 19935

9 5210 1010 30105511 26

12 001257135915091625

17 4219 0020 17

+50°

1) m8549 4010 1110 34•10 50

11 0411 1011 2811 4011 54

12 11123413 0413461442

155017071828195021 10

223123 52

1 102 42

4 095 31G 41733809

8358549 099 21933

9 4595810 14103411 00

11 3712 20133014 4516.06

173018532016

+52°

li in9 099 53102110 411055

11 0011 1011 2011 3611 48

120312 2312 5113311427

153710571821194521 08

223123 55

1 22251

4 215 4f65f7 47820

8439009 129 23'932

9 42953100710 241048

11 2312 1113 16143315 57

1724185020 15

+54°

h m9 201007103210 4«11 00

11 0911 1711 2411 3211 41

11 5412 11123013 1514 10

1522164518 12193921 05

223123 58

1 28301

4356037 M802833

8529009 169 24931

9 399479 5810 131034

11 001 1 5-1130014201548

17 17184620 15

+56°

h in9 47102310 4410 5711 00

11 1211 1711 2211 2711 34

11 4311 5712 1912 541360

15 0416311802193321 03

2232

0 021 353 12

4 616237 35821847

9039 139 209 25930

9 359419 49100010 18

10 4711 33124014041536

17 1018 4220 14

+58°

li in10 1210 4310 5911 0711 12

11 1511 1711 1911 2211 26

11 3111 4111 58122!)132-1

144316 15175219272100

2232

0 001 433 25

5 106488028 449 04

9 14920924926929

931934938940959

102211 0012 1613 461523

1701183820 14

+60°

li m104711 0811 1511 1811 19

11 1811 1811 1711 1611 16

11 1811 2111 311 1 5512 49

14 151556173919 192056

2233

0 111 633 41

6347238419 13924

9289299 29'9 289 27

9 269 269 269 28934

9 5010 2911 4413 231508

1652183320 13

(a) The GMT of moonrise.

Figure 3.- Sample pages from the American Ephemeris and Nautical Almanac (ref. 3).

27

MOONSET, NORTHERN LATITUDES, 1968

LOCAL MEAN TIME OF MOONSET (UPPER LIMB)MERIDIAN OF GREENWICH

^"\ Lat.Date^^-v^

Jan. 01234

56789

1011121314

151C171819

2021222324

2526272829

3031

Feb. ' 123

45078

910111213

141510

0°

h m18411941203021 2522 10

22522332

0 12052

1 352 20309400455

5 506 447378279 15

100110 4811 36122713 21

14 2015 2216 2517 2518 22

19 14200120 4521 262207

22 -1723 2'.)

0 131 00

1 ,r)()2433 384 335 27

6 197 097 57

+ 10°

h m18191922202021 142203

22492334

0181 02

1 492373 294225 17

611703752838921

10 0310 4511 2812 1413 04

13591459100217 0518 05

19011952204021 2622 11

22 fiO23 41

0 291 19

2 113 054 004 53544

6327 17800

+20°

h m17561901200421 0221 56

224723 36

0241 13

2032563 504465 41

6347 248098 509 28

10 0510 4211 2012 001246

133814 35153816431746

18 461943203621 2622 15

23 0523 55

0 4 61 39

2 343 304 245 15602

6 407 26804

+30°

h m17 2818371944204821 47

22432338

0311 25

2203 174 155 136 09

7017478 289 (M9 36

100710 3811 1011 4512 25

13 1214 0715 1016 171724

183019 3220 3021 2622 2J

23 15

0 101 062 03

3 013 584 515 406 23

7017 36808

+35°

h m17 13182319 33204021 42

22422339

0 351 32

2303304 305 29625

7 168008 389 119 11

10 0810 3611 0411 3612 13

125713 5114 53160217 12

18 2019 2520 2721 2622 2-1

23 21

0 191 182 17

3 174 14507554635

7 107 4 28 10

+40°

h m1654180719 20203021 36

22392340

0401 40

242344447548645

7348 168519 209 40

10 1010 3310 5811 2611 59

124013 3214 3415441657

1809'19 1820 2321 2622 27

23 28

0 2(11 312 34

3 354 345 266 11649

7 217 488 13

+45°

h m16311747190420 1921 30

22372342

0461 50

2554025086 11708

7568 359 059 309 52

10 1110 3110 5111 1411 43

12 2013 0814 1015 221C 39

17 5619 0920 1 921 262231

23 36

0 411 472 53

3 584 575 496 317 05

7 337 568 16

+50°

h m160117 22184520 OC21 22

223423 44

0 52201

3 124 235 34640738

8 238 589 239 439 59

10 1310 27104211 0011 23

11 5412 3913 4014 5516 17

17 4018 5920 1421 2622 36

23 46

0 562 073 18

4 265 276 186 567 25

7 478048 20

+52°

h m154717 10183019 5921 18

22332345

055207

3 19433547655752

8 379089319 48

10 02

10 1410 2610 3810 5311 13

11 42122413 2514 421607

1732185420 1221 2622 38

23 50

1 032 163 30

4 405 426 3270S7 35

7 548098 21

+54°

h m15 301656182619 5221 14

22312345

0 592 13

3284456 017 128 10

8529219 419 55

10 06

10 1510 2410 3410 4611 03

11 28120713 0714 2015 55

17 24184920 0921 2622 4 1

23 55

1 102 273 4 4

4 576 006 487 22745

8018 13823

V

+56°

h m15 10164018 14194521 09

22292346

1 032 19

3384586 18732830

9 109 35951

10 0210 Oil

10 1610 2210 2910 3810 51

11 1111 47124614081541

17 14184320 0621 2622 43

0 001 192 393 59

5 166 217087387 57

8 098 188 25

+58°

h m14 451620180019 3021 04

22 282348

1 07227

3 495 14639757856

932952

10 0310 0910 14

10 1710 2010 2410 2910 37

105211 2112 19134615 25

17 0318 3620 0321 2622 46

0 071 292 534 18

5 -106 487327578 11

8 198 248 27

+60°

h m14 101556174419252059

222523 49

i ii235

4025 337058319 31

100010 1110 1610 1810 18

10 1810 1810 1810 1810 21

10 2710 4611 4013 1615 06

16 5118 2919 5921 2622 50

0 i-t1 403 104 42

6 127 258 05820827

8 29830829

(b) The GMT of moonset.

Figure 3.- Concluded.

28

T3

O

Octffl

CO

«HO

o•H-P

in3

210

in110

010

in"110 t

, -210

-, -310

\

-M

s

e1

\

^ L>f

\L

-- V1

-^V-\\\\

\\\v

r\

yv

an illumination of skybackground produced by

starlight, 2.15 x 10~"5

\\

Ivu

\

\\\ff y

V

ss

1 ~,

1090 95 100 . 105

Zenith angle of sun, deg.

110

Figure 4.- Illumination of sky background as a function of the zenith angle of the sun.

29

*o00

£.

CQ r-1 03

: --j 1 1 r -i *~-r -T —

°0•tf

to °0fl ro

30

I

S 131

S.

M 151

T

W 17-

T

F 19-

S

S 21-

M

T 23 -

W

T 25-

F

S 27 -

S

M 29

T

W 31 -

T

F

S

S 41

M

T

W

T

F

S 10

S

M 12

21

6

81

Launch window which insures thatdarkness conditions exist duringlaunch

-Launch vindow which insures thatdarkness conditions exist duringreentry at Q

Launch window which insures thatdarkness conditions exist duringboth launch and reentry

1800 2000 2200 2400 0200 0400 0600

Eastern standard time, hours

16

-18

-20

h22

-24

-26

28

30

1

7

9

11

13

Figure 6.- Launch window which insures that maximum darkness conditions will exist during both launch and660 seconds after launch when reentry occurs at Q.

NASA-Langley, 1969 21 L-6369 31

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